LINear EXponential function: energy as factor of production A USA empirical analysis

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LINEAR EXPONENTIAL FUNCTION:

ENERGY AS FACTOR OF PRODUCTION

A USA EMPIRICAL ANALYSIS

Saverio Barabuffi

Master of Science in Economics

October 2017

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In loving memory of my father To my mother

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List of Figures

1.1 World energy consumption . . . 10

1.2 World per capita energy consumption . . . 11

1.3 Energy per capita consumption for different resources . . . 12

4.1 US GDP time series . . . 34

4.2 US GDP per capita time series . . . 36

4.3 US capital stock time series . . . 37

4.4 US primary energy consumption time series . . . 38

4.5 US average annual hours worked by worker time series . . . . 39

4.6 US numbers of employed time series . . . 40

4.7 US total average hours worked time series . . . 41

4.8 US energy/gdp ratio time series . . . 42

4.9 US energy/gdp per capita ratio time series . . . 43

4.10 US energy/capital ratio time series . . . 44

4.11 US energy/average hours ratio time series . . . 45

4.12 US energy/numbers of employed ratio time series . . . 46

4.13 US energy/total average annual hours ratio time series . . . . 47

5.1 Logarithm real oil prices . . . 51

6.1 Output elasticities with constant parameters . . . 71

6.2 Output elasticities with variable parameters . . . 72

6.3 RTO output elasticities with constant parameters . . . 73

6.4 RTO output elasticities with variable parameters . . . 74

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List of Tables

5.1 US Kummel’s results 1960-1996 . . . 50

5.2 Static model estimates . . . 53

5.3 RTO Static model estimates . . . 54

5.4 Durbin-Watson test statistics for static model . . . 55

5.5 Durbin-Watson test statistics for RTO static model . . . 55

5.6 Cochrane-Orcutt model estimates . . . 56

5.7 RTO Cochrane-Orcutt model estimates . . . 57

5.8 Durbin-Watson test statistics for Cochrane-Orcutt model . . . 57

5.9 Durbin-Watson test statistics for RTO Cochrane-Orcutt model 57 5.10 Augmented Dickey-Fuller test . . . 58

5.11 Augmented Dickey-Fuller test for difference . . . 58

5.12 Johansen procedure with eigenvalue . . . 61

5.13 First-difference model estimates . . . 62

5.14 RTO first-difference model estimates . . . 62

5.15 Durbin-Watson test statistics for first difference model . . . . 63

5.16 Durbin-Watson test statistics for RTO first difference model . 63 6.1 CD and CDE static model regression . . . 66

6.2 CD and CDE Cochrane-Orcutt model regression . . . 67

6.3 CD and CDE first difference model regression . . . 68

6.4 Kummel’s output elasticities 1960-1996 . . . 69

6.5 Averaged LINEX α for different time periods . . . 77

6.6 Averaged LINEX β for different time periods . . . 77

6.7 Averaged LINEX γ for different time periods . . . 77

6.8 Averaged RTO LINEX α for different time periods . . . 79

6.9 Averaged RTO LINEX β for different time periods . . . 79

6.10 Averaged RTO LINEX γ for different time periods . . . 79

6.11 Average output elasticities - LINEX estimates . . . 80

6.12 Average output elasticities - RTO LINEX estimates . . . 81

6.13 Output elasticities - Cobb Douglas estimates . . . 82

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Chapter 1 What is Energy?

1.1 Energy and Thermodynamics

Before analysing energy and its role in Economics and Economic Theory, it is important to understand what is energy and focusing on its definition, but also understand the key concept of thermodynamics from a scientific per-spective.

The term energy was firstly used in 1619 by Johannes von Kepler in ”Har-monice Mundi”, it derives from the Greek word ”en´ergeia” (from ”en” + ”ergon”) and it can be translated in ”within work” or ”dynamic force”, so we can easily define energy as the capability of producing changes.

From a Physicist point of view, energy is the property that must be trans-ferred to an object in order to perform work on or to heat the object; even if energy exists, it is not always possible to use it to do work.

We can find different form of energy: some examples are kinetic, potential, mechanical, electric, magnetical and nuclear energy.

While we define heat and work as forms of transit of energy.

A relevant branch of physics is Thermodynamics (from the Greek ”thérmé” and ”dúnamai”), a science that was born with the invention of steam engine by Thomas Savery in 1697 and Thomas Newcomen in 1712.

Thermodynamics is related to the study of all forms of energy and their transformations and mutual actions between energy and matter , which are governed by the Laws of Thermodynamics.

The focus is on the First and the Second Law of Thermodynamics, de-veloped in the 1850s by William Rankine, Rudolf Clausius and Lord Kelvin. The First Principle of Thermodynamics is the ”energy conservation

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8 CHAPTER 1. WHAT IS ENERGY? ciple”, a basic principle of nature which is satisfied by chemical reactions: energy cannot be neither created nor destroyed, but it can changes forms and flow from a one place to another.

Energy is a physical quantity which generally remains constant.

This principle does not imply any limitation on converting energy from a condition to another, it derives from the possibility to transform work in heat and viceversa.

However, independently from the First Principle, the conversion from heat to work seems limited and the Second Principle acknowledges this applied impossibility.

The Second Law of Thermodynamics relies on the fact that energy, be-sides quantity, has quality and that real processes tend to reduce the quality of energy; in simple words: energy tends to deteriorate and change into a less useful form.

The Second Law allows to determine the theoretical limits of energy conver-sion systems.

1.2 Exergy and Entropy

Since the Laws of Thermodynamics are important under economic perspec-tives because industrial production is deeply related with energy conversion, it is essential to emphasise the concept of Exergy, Entropy and Enthalpy. Energy can be seen as be made up of two element, an antropomorphic dis-tinction: Exergy and Anergy.

On one hand, Exergy is defined as the energy available to use, from which it is possible to obtain the maximum work of a process.

On the other hand, Anergy is the useless energy produced in an energy con-version process at the expenses of valuable exergy.

During an irreversible process, Exergy is destroyed.

We then can define Entropy, available energy continously transformed into unavailable energy , until it dissipates, it disappears entirely.

In order to be clear, entropy will not be illustrated under a quantitative ap-proach, the focus is on its broader qualitative meaning.

Entropy is a thermodynamic function that grows in relation with the dis-order level of a system.

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1.3. ENERGY IN MODERN AND CONTEMPORARY HISTORY 9 Entropy constantly increases in relation to the disorder level of every irre-versible transformation, since in the economic system energy is involved in economic process which are irreversible, energy becomes a relevant factor of production.

Exergy and entropy are complementary physical quantities, since entropy is a complex and difficult concept to be interpreted, exergy has been intro-duced for its simple understanding.

Under the light of this two concepts, energy became a precious factor for the economic process due to its change in quality related to the energy conversion.

1.3 Energy in Modern and Contemporary

His-tory

Vaclav Smil, in his seminal paper ”Energy in the 20th century: resources, conversions, costs, uses, and consequences”, defines the 20th century as the era of the first high-energy civilization, since fossil fuels became the dominant sources of world’s primary energy.

High-energy civilization defines an era of fundamental innovation followed by rapid growth due to mass diffusions of essential innovation, technical inno-vation that ”has been responsible for impressive growth of capacities, flexibil-ities, and efficiencies of energy convertors, as well as advances in exploration, extraction , transportation and transmission”1

Technical innovation and invention, such as steam turbine, electric motor and internal combustion engine, brought to an increase of efficiency in en-ergy conversion.

Even if during the last century energy conversion has been increased, energy consumption rose.

In order to understand the increase of world energy consumption of fossil fuels, it is possible to plot a 1820-2010 time series for energy consumption by using as source estimates of Vaclav Smil from his 2010 book ”Energy Transitions: History, Requirements and Prospects” and British Petroleum Statistical Data from 1965 to 2010.

1_{Vaclav Smil, 2000, ”Energy in the 20th century: resources, conversions, costs, uses,}

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10 CHAPTER 1. WHAT IS ENERGY?

Figure 1.1: World energy consumption

Figure 1.1 shows the exponential growth of World energy consumption that started from the late 19th century and which took-off during the World Wars years, while from 1950s to 2010 energy consumption quintupled (from 100 exajoules to more than 500 exajoules).

Until the 1960s the dominant sources of energy were biofuels and coal,the key sources of energy consumption in under-developed countries.

After World War II, with insignificant oil extraction costs in the Persian Gulf and the discovery of more and more oilfield, oil rapidly replaced carbon as the most important energy sources.

From 1950s, with an increase of energy demand, driven by Europe’s post-war reconstruction and the developed of automobile mass-consumption mar-kets, oil became more and more important in the world energy balance. Use of coal has remained at most equal until the end of 1960s, but it in-creased during the 1970s oil crisis in which it became a substitute for oil in electricity production.

Even after the oil crisis, coal mantains a sustained growth as primary source for energy consumption since it became fundamental for the economic growth of developing countries, such as China and India.

From 1970s, the use of natural gas, hydro-electric and nuclear generation of electricity became more and more important in relation with the increase of oil prices, but their use remain at most constant until 2010.

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1.3. ENERGY IN MODERN AND CONTEMPORARY HISTORY 11

Figure 1.2: World per capita energy consumption

Figure 1.2 shows average consumption per person as a result of combin-ing previous energy estimates with population estimates provided by Angus Maddison.

From 1820 to 2010, population rose from 1 billion to 7 billion, having an exponential increase after World War II; increase of population led to an increase of per capita energy consumption.

Until the beginning of World War I, there is not an increase of per capita energy consumption, meaning that coal offsetted the use of other fuels. Small increase of per capita energy consumption happened during World War I and from 1990s, while it increased the most between World War II and 1970s.

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12 CHAPTER 1. WHAT IS ENERGY?

Figure 1.3: Energy per capita consumption for different resources In order to understand the per capita consumption of each resource, in figure 1.3 are showned the resources individually without stacking them as in the previous figures.

Standard biofuels are not take into account, while are taken into account modern biofuels as BP-other.

Coal per capita consumption increased from the dawn of the Second In-dustrial Revolution, but its use remained constant from World War I until 2000s, then increases again in relation with Chinese economic boom.

As told before, oil has become the most important fossil fuel, but from 1970s natural gas has been a substitute for oil in electricity generation and home heating.

While hydro-electric, nuclear and modern biofuels even if they had an in-crease in the last decades, they play a marginal role in energy consumption.

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Chapter 2 Energy in Economic Theory

2.1 Neoclassical growth theory

Since the 19th century, growth was attributed to capital accumulation and labor force growth, the in the 1920s, a Russian economist, Grigorii Fel’dman introduced the identity between th rate of growth of the economy to the savings rate divided by 4capital/4output ratio as a result of a two sector growth model based on Marxist’s thought and heavy industry of the new-born Soviet economy.According to Feldman, greater the proportion of new investment in the producer goods sector, the higher the rate of growth of the entire economy.

This identity was later suggested by Roy Harrod in 1939 in ”An essay in dynamic theory” and by Evsey Domar in 1946 in ”Capital expansion, rate of growth and employment”, the model developed later became famous as the Harrod-Domar model.

They both ended with the same result, trying to investigate different aspects of long-run growth rate and a ”growth conservation”.

Harrod examined the self-adjustment of the economic system over an instable steady state. Capitalism is seen as a production system that moves towards growth or stagnation.

Harrod describes the ”Fundamental Equation” as s

v =

Yt+1− Yt Yt

= gy(t) = gw(t) (2.1)

where gy(t) is the geometric rate of growth of income or output of the system, while gw(t) is warranted rate ofincome growth that will mantain the same rate of growth, s is the fraction of income settled by individuals and firms

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14 CHAPTER 2. ENERGY IN ECONOMIC THEORY to savings and v is the value of capital goods required to produce a unit increment of output.

On the other hand, Domar focused on the existence of a steady state for investment, in order to have full employment of productive capacity.

Domar then assumed a full employment of productive capacity and describes the ”Fundamental Equation” as

s

v = gI(t) = gk(t) = gy(t) (2.2) Investment, capital and output must grow at the same rate _vs in order to have effective demand equal to productive capacity.

The result of both models is the same, even if reached independently, they both share the equation which states a constant growth rate in order to realize full employment of productive capacity, nowadays referred as the Harrod- Domar fundamental equation

gy = s

v (2.3)

2.1.1 Solow Model

Since the 1956 seminal papers ”A Contribution to the Theory of Economic Growth” of Robert Solow and, growth theory has been focused on technical progress as driver of economic growth.

The work of Robert Solow is based on the Harrod-Domar model assumptions, over a single sector with two factors (capital and labor) under standard neo-classical conditions.

The Solow model can be seen as an evolution of the Harrod-Domar model, since it is based on factor subsitutability, where market mechanisms can mod-ify gy = _vs.

In the model are assumed many price-taking firms in equilibrium, producing a single composite product (output), constant return to scale, possibility of substituting labor for capital in production, and viceversa, and a homoge-nous of first degree production function.

According to this assumptions, if factor shares are constants, they can be interpreted as output elasticities.

Neoclassical production function must also satisfy constant return to scale property, positive and diminishing returns to private inputs, Inada conditions and essentiality of inputs.

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2.1. NEOCLASSICAL GROWTH THEORY 15 In 1956, Solow described the production function as

Yt = F (Kt, Lt, t) (2.4)

without specifying a mathematical form.

In 1957, Robert Solow in ”Technical Change and the Aggregate Produc-tion FuncProduc-tion” specifies a Cobb-Douglas producProduc-tion funcProduc-tion with capital and labor as inputs, but in which it appears an exogenous variable A(t), which reflects technological change and it depends on time.

Techincal change is considered as related to time, and output increases with time, taken the other factors ceteris paribus. The production function can be re-written as

Yt= A(t)F (Kt, Lt) (2.5)

Technical change has been seen in different ways, by different scholars: • according to John Hicks, technical change is neutral when the marginal

productivity of labour and capital is raised in same proportion;

• Joan Robinson opened to the idea of a biased technical change, which can be capital-saving or labor-saving;

• according to Roy Harrod, techincal change can be neutral, capital-saver or capital-user;

• according to Robert Solow, technical change is labor-augmenting since it increases labor productivity.

Besides mathematics, Solow provides an application to US vintages from 1909 to 1949, based on Raymond W. Goldsmith estimates, and reconstruct technical change time series.

According to Solow, innovation, so technological change, must be embodied in new capital, but it raises problems of measurability.

In 1954, according to Solomon Fabricant’s ”Economic progress and economic change”, cited also in 1957 Solow’s work, only 10% of US 1871-1951 economic growth could be explained by capital accumulation.

Since neoclassical production function need to satisfy constant return to scale, so production function must be a first order degree homogenous func-tion, it was necessary to adopt the time-dependent variable A(t) in order to explain the 90% increase in output per capital and attribute it to technical progress.

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16 CHAPTER 2. ENERGY IN ECONOMIC THEORY Technical progress is measured as a residual, once measured productivity of the other factors, and we define it as Solow residual everything that is not explained by capital accumulation, labor productivity.

Nowadays, Solow residual is also known as a ”measure of ignorance”, ”manna from heaven” or simply Total Factor Productivity (TFP).

2.1.2 Endogenous technological progress

In the 1980s, it started an attempt to overcome the Solow model limitations by modifying the assumption of diminishing returns to capital.

The aim was to endogenize standard theory and to reflect observed charac-teristics of real world, since the convergence prediction to a long run steady state of Solow model, between poor and rich countries, was not supported by evidence of a ”catch-up” by developing countries.

Exogenous TFP became outdated, economists try to explain residual as an endogenous device explained by learning by doing, learning by using, economies of scale and accumulation of knowledge.

In order to explain endogenous growth, it is central to explain the ”AK model”.

AK model in which variable K includes both capital in strict sense and hu-man capital, in order to avoid diminishing capital returns to scale.

In this approach, technological knowledge is a non rival good and human capital compensates the declining returns of capital by taking into account influence of factor augmenting and technological spillovers, since technologi-cal spillovers are externalities able to increase the return to stechnologi-cale.

Since K can be accmulated and output is not subject to diminishing returns, growth can continue indefinitely. Knowledge, social learning and development of human capital became an explanation for economic growth, but a qualitative and theoretical explanation.

Human capital is not directly quantifiable, as information, but it has been a focus for economics research for decades.

2.2 1970s Oil crisis and substitutability

During the 1970s, we had two oil crisis, that brought to an increase of energy prices. In 1973, following the United States of America involvement in the Yom Kippur War (the war between, on one hand, Israel and, on the other

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2.2. 1970S OIL CRISIS AND SUBSTITUTABILITY 17 hand, Egypt and Syria) the Organization for Arab Petroleum Exporting Countries (OAPEC) decided to cut down production of oil and an embargo pointed towards the USA and every western country which was supporting Israel.

The decision of the Arab countries led to a 5% reduction of monthly pro-duction of oil and it led to an increase of Arab oil price, barrel oil prices quadrupled at global level.

Besides the effects of stagflation due to this negative supply shock and the cut of interest rates by Central Banks, the oil crisis opened a debate in economic theory regarding substitutability among non-renewable natural resources and capital.

In 1974, this debate end up with the seminal papers of Solow, Stiglitz, Das-gupta and Heal published on Review of Economic Studies.

Summing up their results:

• according to Solow, substitutability is feasible and it allows, under certain conditions (e.g. no extraction costs, non-depreciating capital and elasticity of substitution between capital and resources is equal to unity), to achieve economic sustainability, that is, exhaustible resources do not constitute limits to growth;

• according to Stiglitz, under strong and increasing resource-augmenting exogenous technological change, sustitutability might allow growth and enable economic sustainability;

• according to Dasgupta and Heal, introducing uncertainty on discover of new knowledge and essentiality in exhaustible resources bring to unsustainable results.

Neoclassical growth theory does not take into account technical limits, it does not allow for limits on substitution and technological progress, but also it does not account for energy and its role in production processes.

Even adding energy in a Cobb-Douglas production function, so describing an energy-dependent Cobb Douglas function, under the essentiality condition if elasticity is unity amount of energy can be infinitesimal if sufficient capital and labor are applied.

In 1979, Edward F. Denison, a pioneer of growth accounting and of mea-surement of US GNP, wrote a paper ”Explanation of declining productivity growth”, published on ”Survey of Current Business” of the Bureau of Eco-nomic analysis.

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18 CHAPTER 2. ENERGY IN ECONOMIC THEORY The paper was focused on the effect of the oil crisis and the rise in energy prices on the US economy.

According to Denison, the effect of the increase of imported oil price has de-creased the National’s command over goods and services, so affecting trade. But it also had the Government put a control over fuel consumption and choice of fuels and it also caused a less usage of energy per unit of capital, labor and land for non-residential activity.

In this paper energy is seen only as a product of labor, capital and natural resources, but it provided an example of treating energy as an input.

The effect of an output per unit of input depends on the elasticity of sub-stitution between, on one hand, energy and, on the other hand, labor and capital and Denison assumed elasticity as unity.

The example reports that energy represents only the 5% on total inputs, and according to a 1% reduction of energy consumption, taking as constant labor and capita, output will be reduced only of 0,05%, being as a base of the cost share theorem that will be explained in chapter 3.1.

By taking into account law of thermodynamics, and moving a step far-away from neoclassical production theory, we can identify thermodynamic limits to substitution, for which it is required a minimum quantity of energy to transform matter, so energy becomes a critical factor for economy.

On the other hand, energy in mainstream economics, but also materials, has always been an intermediate factor of production, leaving the podium of primary inputs to capital, labor and land.

2.2.1 Elasticities of substitution

In economics, it is usual to talk about elasticities of substitution referring to Hicks’s elasticity of substitution, which it applies two inputs formula to each pair of inputs, holding other inputs constant, to measure changes in factor ratios.

Later, Allen developed the partial elasticity of substitution, now defined as Allen elasticty of substitution (AES) which is related to cross-price elasticity (CPE).

Both elasticities estimates, AES and CPE, are provided by studies who refer to elasticity, it is possible to focus only on CPE.

CPE measures the percentage change in demand for a factor due to a per-centage change in price of another factor.

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2.2. 1970S OIL CRISIS AND SUBSTITUTABILITY 19 the cross-price elasticity as:

CP EKE =

dln(K) dln(pE)

(2.6) The main drawback of the CPE is related to the one-input-one-price nature of the elasticity and it does not measure changes in factor ratios.

During the 1960s, Morishima, and, independently, during the 1970s Black-orby and Russel, developed the now called Morishima elasticity of substitu-tion (MES). MES is given by the difference between CPE and price elasticity of one factor; referring to capital and energy:

M ESKE = CP EKE− P EE (2.7)

where CP EKE is the cross-price elasticity for capital and energy, while P EE is the price elasticity for energy. MES can possibly be re-written as

M ESKE = dln(K) dln(pE) − dln(E) dln(pE) = dln( K E) dln(pE) (2.8) MES, as the Hicks elasticity of substitution, is a two-inputs-two-price elas-ticity, since pK is held as constant.

It measures a percentage change in the capital/energy ratio and,conversely to Hicks’s elasticity, it is asymmetric, so M ESKE 6= M ESEK

If MES is negative, an increase in price of energy implies a decline in demand for capital larger than the decline in demand for energy, while a positive MES implies an increase for demand of capital greater than the decline in demand for energy.

A positive MES implies a substitution towards capital.

It is possible to differ between substitution and income effect

• substitution effect measures the direct change in demand for K due to a change in price of energy;

• income effect measures a change in demand for K due to a change in income derived from a change in price of energy, and it is given by the difference between CPE and MES.

The focus on elasticity of substitution between capital and energy is re-lated to the degree of technological flexibility, under the adoption of energy-saving technologies.

Understand the relationship between capital and energy it is central to assess the different impacts of policy designs.

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20 CHAPTER 2. ENERGY IN ECONOMIC THEORY

2.2.2 Limits to Growth

In 1972, one year befor the crisis, Donella Meadows et al. published the book ”The limits to growth”, a work commissioned by the Club of Rome, an environmental NGO.

The book opens by addressing the idea of exponential growth, a dynamic phenomenon which involves elements that change over time, the increase by constant percentage in a constant time period.

Before 1970s, population, food production, industrialization, pollution and conumsption of non-renewable resources increased with an exponential growth, a common process in biology, but also finance.

In order to sustain this exponential growth, it is necessary, on one hand, to support phisical necessities related to physiological and industrial activity, and, on the other hand, support social necessities.

Economic process is seen as a complex systems, in which there are circu-lar and interlocking relationships among the components, in a feedback loop. according to this vision, natural resources and energy are deeply intercon-nected with economic and population growth.

World usage rate has grown exponentially, driven by feedback loops gener-ated by capital and population growth, but it rapidly reduces the fixed stock of resources.

In relation to technology, the book uses an approach that work against the optimistc view of technology. Technology is not seen as a continous mech-anism to raise physical limits indefinetely, on the contrary is not taken into account on the model developed by Meadows et al. since technology cannot be seen as an aggregate variable because it arises from and it influences dif-ferent sectors.

The book critics the view of unlimited and abundant energy resources to sustain economic growth, without taking into account waste and pollution.

2.3 Georgescu-Roegen perspective

The work of Nicholas Georgescu-Roegen can be seen as the starting point of Ecological economics.

He criticized the standard theory vision of the possibility of finding new energy sources and the Pigouvian notion of a stationary state in which pro-duction factors are a stock, an unchanging amount.

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2.4. JEVONS’S PARADOX, REBOUND EFFECT OR KHAZZOOM-BROOKES POSTULATE21

According to Georgescu-Roegen thought, Economy is governed by the Second Law of Thermodynamics, the Entropy Law. The economic process is irreversible and irrevocable and it can be seen as transformation of valuable matter into waste, or as Georgescu defines it ”transformation of low entropy into high entropy”.

He also pointed that energy must be accessible in order to have a value, introducing the ”Energy returns on energy investment” (EROEI) idea:

• it is viable to use a certain technology or resource, only if it led an energy return surplus in order to cover the energy investment.

2.4 Jevons’s Paradox, rebound effect or

Khazzoom-Brookes postulate

As a result from the previous chapter, it is possible to see an increase in en-ergy consumption; from a theoretical point of view, in 1865, William Stanley Jevons focused his work on coal consumption and fossil energy resources and noted that when resource efficiency increases, then the cost of using the re-source decrease and this leads to an increase in consumption of the rere-source, ending with the depletion of the resource itself and the expolitability at rea-sonable costs.

The resource demand increases subsequently to a rise in the production level due to the increased efficiency. Jevons brought the example of the introduc-tion of the steam engine and the parallelism between technical improvement and acceleration in the consumption of coal.

According to the Jevons’s Paradox, an exponential rate of resource consump-tion acts as a time constraint.

Jevons simply described what now it is called ”rebound effect” and which focus on energy and energy efficient technology. Efficiency brings more users since it decreases energy costs.

In 1980, Daniel Khazzoom analyzed the rebound effect from a micro-level perspective, by decomposing the price reduction, a direct effect or pure-price effect, into income and substitution effect.

It is also possible to distinguish among short and long run.

In the short run we can assume a cost minimizing behaviour; a reduction of effective price of energy services induces firms to substitute energy with other factor input, substitution will increase output. Taking into account

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22 CHAPTER 2. ENERGY IN ECONOMIC THEORY that substitution among energy and capital can be limited by short run pro-duction behaviours, it could be that diminishing returns to increasing uses of energy will provide input substitution in favor of energy and increasing energy consumption, but due to limit on substitution it could end up with a rebound effect equal to zero.

In the long run, there are no constraints on factor substitutability and we can assume an output maximization behaviour, a reduction of energy services prices will induce an immediate increase in size of industry and an increase in demand for energy. These long run effects are economy-wide effects. The reduction of energy prices can also have secondary effects. From a con-sumer perspective, an increase of real income will increase demand of other goods and services. The effect on economic growth will depend on the shares of consumer’s income or expenditures devoted to energy services.

From a firm perspective, a reduction of cost for energy factor will increase demand for other inputs.

Both secondary effects are expected to be minor or insignificant.

In 1990, Leonard Brookes linked the microeconomic aspects of the re-bound effect with the macroeconomic side of energy consumption increasing. According to Brookes an increase of use of higher quality forms of energy has improved technical change, and so total factor productivity (TFP), and also driving economic growth.

He also stated that an individual energy efficiency improvement decreases the effective price of output energy (or useful work), while it does not affect energy prices that remain constant.

In 1992, Harry Saunders developed the so called ”Khazzoom- Brookes Postulate”: with fixed real energy prices, the energy efficiency gain will in-crease energy consumprion above what it would be without this gain”. According to Saunders, the Jevons’s Paradox is supported by neoclassical production and growth theory.

By specifing a Cobb-Douglas production function with three inputs (capital K, labor K and energy E) and by introducing an energy-augmenting tech-nology progress (γE parameter)

Y = f (K, L, γEE) (2.9)

it is possible to specify energy conservation as the elasticity of energy use with respect to the energy-augmenting technological progress parameter

ηE_γE = dlnE dlnγE

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2.4. JEVONS’S PARADOX, REBOUND EFFECT OR KHAZZOOM-BROOKES POSTULATE23 The rebound effect is simply given by adding 1 to the value of energy

con-servation

R = 1 + η_γEE (2.11)

We can distinguish among rebound effect and backfire, according to the value of R:

(

0 < R ≤ 1 Rebound R > 1 Backf ire

In order to understand the inadequacy of neoclassical production func-tion, in relation with with Jevons Paradox, it is possible to address the example provided by Philippe Aghion and Peter Howitt in their 2008 book ”The Economics of Growth”.

They start assuming a one sector AK model with an exhaustible resource

Y = AKRφ (2.12)

In this model, both capital and resource are falling to zero in the long run, but also output will eventually fall to zero, both the growth rate and the level itself.

This model, in order to sustain growth, brings to a crossroads:

• flow of extracted resource becomes small as time goes to infinity, oth-erwise resource stock and output flow will become zero;

• increase of technical progress.

The main drawback of techincal progress is the requirement of capital accu-mulation, so an acceleration of production with resource consumption that eventually leads to an exhaustion of the resource.

Even if the focus is on an exhaustible resource, it is possible to address it to energy consumption since energy is deeply related to exhaustible resources. The rebound effect has been seen under a theoretical light by many schol-ars, but Polimeni in his 2006 article ”Jevons’ Paradox and the myth of tech-nological liberation” has tried to statistically analyse at a macro level the relationship between energy consumption and energy efficiency.

He described the EC = P AT model, in which I is total primary energy con-sumption, P is percentage change in population, A is percentage change in GDP and T is percentage change in energy intensity.

In order to support evidence for macro-level manifestation of Jevons’ Para-dox, Polimeni used two different time-series cross-sectional (or panel data)

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24 CHAPTER 2. ENERGY IN ECONOMIC THEORY model.

The first one is

EC = β1+ β2A + β3T + β4P ; (2.13) while the second one

EC = β1 + β2A + β3T . (2.14)

He provided an analysis for six different world regions (North America, Cen-tral and South America, Western Europe, Asia, Africa and Middle East) and covering 92 nations in a time period from 1980 to 2002.

Jevons’ Paradox has been proved for all 6 regions, but with different resulats over the macro-variables that push the energy consumption.

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Chapter 3 The LINEX Function

From chapter 2.1, it is clear the need of a model which tries to explain eco-nomic growth without involving qualitative variable, such as human capital and technological progress.

This need for a quantification can be seen under the light of introducing energy as third factor of production, since energy is a quantitative variable and it was, and still is, fundamental in economic development and economic growth.

In 1982, Reiner Kummel, in his work ”The impact of energy on industrial growth”, made the assumption that energy is the nature’s driver of change and that capital and labor are the instruments to direct energy, to make it available and to process information.

Capital, labor and energy are interdependent and their ”cooperation” is nec-essary to understand economic growth.

The work of Kummel can be seen as a merge between neoclassical theory and energy economics.

Behind the model of Kummel relies the fact that capital stock is simply energy-conversion and information-processing devices and buildings and in-stallations used for the devices protection and operation.

Kummel gives a more articulate definition of capital than looking at it only as a productive input that is produced and it provides an ongoing stream of productive services.

Capital to be activated, to be productive needs to be activated by exergy or useful energy, but it also needs human labor in order to be supervised, organized and allocated.

Labor can be divided in two components:

• routine labor - it can be substituted with a combination of energy and 25

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26 CHAPTER 3. THE LINEX FUNCTION capital;

• creativity - contribution to growth and production that cannot be per-formed by machines

In his vision, materials and land do not play any active role in the production process seen as work performance and information processing. Since we are dealing with a static growth model, its aim is to explain ho growth occured and not how it will occur.

According to Kummel, energy plays a bigger role with respect to its cost share. His point is related to the fact that production factors are technolog-ically constrained.

In an environment in which there are not technologically constraint, such as neoclassical growth theory, factor’s output elasticities are equal to its cost share.

Taking into account a production function for one sector, with three fac-tors

Y = [K, L, E; t] , (3.1)

where Y is the output, K is the capital, L is the labor, E is energy and t is time.

We can state the total differential of the production function: dYt= ∂Yt ∂Kt dKt+ ∂Yt ∂Lt dLt+ ∂Yt ∂Et dt +∂Yt ∂t dt , (3.2)

then we divide the toal differential of the production function for Y and multiply and divide each factor partial derivative for their relative factor, obtaining: dYt Yt = Kt Yt ∂Yt ∂Kt dKt Kt + Lt Yt ∂Yt ∂Lt dLt Lt +Lt Yt ∂Yt ∂Et dEt Et +t − t0 Yt ∂Yt ∂t . (3.3)

Defining that output elasticities as the weights by which marginal relative changes of production factors contribute to the marginal relative change of output; output elasiticities can be expressed as:

α ≡ Kt ≡ Kt Yt ∂Yt ∂Kt ; (3.4) β ≡ Lt ≡ Lt Yt ∂Yt ∂Lt ; (3.5)

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27 γ ≡ Et ≡ Et Yt ∂Yt ∂Et (3.6) δ = t − t0 Yt ∂Yt ∂t (3.7)

α is the output elasticity of capital, β of labor, γ of energy and δ of creativity. We can write the growth equation as:

dYt Yt = αdKt Kt + βdLt Lt + γdEt Et + δ dt t − t0 , (3.8)

and since there are not technological constraints, we obtain a Cobb-Douglas energy dependent production funcion

YCDE = KαLβEγA , (3.9)

α, β and γ = 1 − α − β are equal to the cost share of each factor and satisfy the constant returns to scale

This view is satisfying under a national accounting perspective, since output elasticities are seen as factor shares for capital and labor, respectively α and β, constructed on payments on capital and labor in national accounts. Kummel moves further his critique by adding factor-dependent output elas-ticities.

In order to derive a unique function of factors, the production function Y=[K, L, E; t] must be twice differentiable in order to have a continuous function, meaning that its second-order mixed derivatives for K, L and E must be equal ∂2_Y t ∂Kt∂Lt = ∂ 2_Y t ∂Lt∂Kt ; (3.10) ∂2_Y t ∂Kt∂Et = ∂ 2_Y t ∂Et∂Kt ; (3.11) ∂2_Y t ∂Lt∂Et = ∂ 2_Y t ∂Et∂Lt . (3.12)

From these three equations we obtain three differential equations: K ∂β ∂Kt = Lt ∂α ∂Lt ; (3.13) Kt ∂α ∂Kt + Lt ∂α ∂Lt + Et ∂α ∂Et = 0 ; (3.14)

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28 CHAPTER 3. THE LINEX FUNCTION Kt ∂β ∂Kt + Lt ∂β ∂L + Et ∂β ∂Et = 0 . (3.15)

According to the law of diminishing returns, an additional unit of capital will contribute less than proportionally to output growth, while decreasing marginal output.

Since capital requires energy to be used, to produce and it requires a certain amount of labor to be handled, an additional unit of capital will decrease additional output only if the ratio of energy and labor over capital decreases. α decreases with the ratio of energy and labor over capital and it also satisfies the asymptotic boundary conditions

α → 0 if Lt+ Et Kt

→ 0 . (3.16)

In a growing automation production environment, we define capital stock working at full capacity as KM. In a state of maximum automation, capital requires the energy quantity EM

EM = ctKM , (3.17)

in which ctis the energy-demand parameter of fully employed and maximally automated capital stock. It becomes time dependent when innovation affects the energy demand of fully employed capital.

ct is deeply interconnected with the energy efficiency of capital stock, ct de-creases if energy efficiency inde-creases, and conversely.

In order to satisfy the asymptotic boundary conditions, output elasticities must tend to zero such as capital approaches to its maximum automation capacity KM

β → 0 if K → KM and E → EM = ctKM . (3.18)

In order to develop the new output elasticities, Kummel introduces the parameter at.

at described as the capital effectiveness related to the contribution of energy and labor to capital ratio to output elasticities, it is the effectiveness with which energy activates, and labor handles, the capital stock and, as ct, it is time-dependent with innovation.

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3.1. COST SHARE THEOREM AND SHADOW PRICES 29 The three output elasticities that satisfy the constant return to scale (α+β+γ=1), the asymptotic boundaries and the differential equations are:

α = at L_t+ E_t Kt , (3.19) β = at c_tL_t Et − Lt Kt , (3.20) γ = 1 − at Et Kt − atct Lt Et . (3.21)

The three output elasticities depend on three variables and they change over time.

While α reflects a hypotetical capital-intensive state, β reflects substitution of labor provided by capital and energy provided by increasing automation. Combinations of factor reflects the avoidance of a decrease of output due to a marginal increase of an input, so output elasticities must be non-negative

α ≥ 0, β ≥ 0 and γ = 1 − α − β ≥ 0 . (3.22) Since we characterized atand ctas function of time, it is possible to treat the technological progress A equal to unity, then inserting the output elasticities in the growth equation of the Cobb-Douglas production function, we obtain

dYt Yt = at L_t+ E_t Kt dK_t Kt + a c_tL_t Et − Lt Kt dL_t Lt + 1 − aEt Kt − atct Lt Et dE_t Et . (3.23) By integrating the growth equation with the factor dependent output elas-ticities, we obtain the LINEX (LINear EXponentially )function, which is linearly dependent from energy and exponentially from ratio of the three factors (capital, labor and energy)

Yt = Et× exp n at× h 2 − Lt+ Et Kt i + atct× L_t Et − 1o . (3.24)

3.1 Cost share theorem and shadow prices

In order to better understand the differences of an equilibrium condition between an unconstrained maximization besides a constrained .

By considering an economic system with three factors (K is capital, L is labor and E is energy), we can describe the factor vector as X = (XK, XL, XE). Price vector is p = (pK, pL, pE).

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30 CHAPTER 3. THE LINEX FUNCTION Since factors costs are simply given by their prices multiplied by the factors, we can easily write the factor cost vector as:

p ∗ X ≡ (pKXK, pLXL, pEXE). (3.25) We can maximize profit G = Y − pX subject to a constraint, by introducing a slack variable fA as technological constraints, necessary condition is:

OY − piXi+ X

a

µafa = 0 (3.26)

O is the gradient in factor space and µa are the Lagrangian multipliers. The gradient implies to compute partial derivatives for each factor, but in order to simplify the calculus we define a general case in which we show pi and Xi where i = K, L, E. The result of the partial derivatives with respect to Xi is

∂Y ∂Xi − pi + X a µa ∂fa ∂Xi = 0 (3.27)

Multiplying the last equation with Xi_Y , in order to obtain factor elasticities: Xi Y ∂Y ∂Xi ≡ i = Xi Y h pi− X a µa ∂fa ∂Xi i (3.28) In order to mantain the constant returns to scale assumptions, the sum of elasticities must be equal to unity

X

i

i = 1; (3.29)

then it is possible to obtain the output Y Y =XXi h pi − X a µa ∂fa ∂Xi i . (3.30)

In order to understand the weight of shadow prices in a technologically con-strained maximization we need to insert Y in (3.28)

i = Xi h pi −P_aµa_∂Xi∂fa i P Xi h pi− P aµa_∂Xi∂fa i . (3.31)

In a unconstrained maximization, µa = 0, so from the previous equation we obtain:

i = piXi P piXi

= piXi

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3.2. TECHNOLOGICAL CONSTRAINTS 31 It has been possible to show the so-called cost share theorem, from which neoclassical production theory infers an equivalence between output elastic-ities and factor cost shares.

Assuming technological constraints, µa6= 0, we can describe the shadow prices as: si = −µa ∂fa ∂Xi , (3.33) so (3.31) becomes i = Xi h pi+ si i P Xi h pi+ si i = Xi h pi+ si i

T otal f actor cost + T otal f actor shadow cost (3.34) Output elasticities become dependent on factors cost share and on shadow prices of constraints.

Shadow prices become a limit to the range of substitution, and this leads to a different form of production function which is the LINEX production function.

3.2 Technological constraints

In the previous section, it has been demonstrated the presence of shadow prices in a constrained maximization, but it is better to explore the techno-logical constraints that previously we have denoted as a slack variable fa. Since the focus is on production, the technological constraints that will be analized are capacity utilization and automation.

Technological constraints limit the substitution between production factors.

3.2.1 Capacity utilization

Capacity utilization represents a technical limit to which is impossible to produce more without meeting increasing costs reflected by a change in the structure of plant or equipment used.

This maximum is related to the the production system, which it cannot operate above his design capacity.

Capacity utilization has its economic counterpart that can be seen as the realized potential output.

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32 CHAPTER 3. THE LINEX FUNCTION

3.2.2 Automation

Automation is the degree of substitution of capital and energy for routine labor.

According to Kalecki, capital should have increased proportionally to the increase in labor force and its productivity.

Within automation process, we can say that increase in capital decreases la-bor force, installed capital has been more and more automated and automa-tion has involved, and it involves, an increasing use of energy and capital inputs, but less labor inputs.

Automation can be seen as an evolution of mechanization; while mechaniza-tion replaces human tasks with machines, automamechaniza-tion involves the entire process, integrating several operations.

While, in 18th and 19th century, on one hand mechanization drove work-ers from countryside to the cities, with the creation of new jobs in the factory environment, on the other hand automation, but also globalization, led work-ers from the manufacturing sector to the service one.

In the past, machines were tools to increase productivity of workers, leading to an increase in wages: technology led to an increase in income.

Nowadays, it is possible to address that, under the automation wave, ma-chines have become workers.

Initially, this transformation of the economic process has been seen as a threat only to unskilled workers, that perform routine and repetitive jobs, but the increasing capability of software and algorithms has been a threat also to predictable jobs of skilled professionals.

Through the ”industrial era”, new technologies led to a less-labor intensive production processes, but what could happen to an economic system? Will long-term unemployment be fuelled by labor-saving innovation? Will it be possible to sustain economic growth within a dystopian jobless economy? It is important to understand that mass-consumption drove economic growth, but what could happen if middle-class sees his income reduced or completely cut-off by the advent of increasing automation?

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Chapter 4 USA empirical analysis

I decided to analyse the United States of America from 1960 in order to under-stand the impact of mass diffusion fundamental innovation, from computer to automated production, and their impact on growth by considering the use of primary energy as factor of production by trying to estimate econometrically the technological parameters of the LINEX function and its output elastici-ties, and comparing the results with the Cobb-Douglas production functions, the simple one (capital and labor) and the one augmented with energy.

The 1960s were the decade of the begininning of the Apollo program and birth of environmental movements that follows the 1950s ”American way of life”.

The 1950s were a decade in which a middle class was created, developing the so called mass-consumption trend, so the 1960s have already faced the well established capitalistic behaviour of the American way of life.

The time period under analysis also faces the most important economic cri-sis, the 1970s oil crisis and the 2007-2008 financial crisis.

Between these two crisis, American economic growth has faced a conti-nous increased prosperity, a growth based on natural resources exploitation and energy use.

Without enter into the debate on the 1980s Reaganomics over the budget deficit, public debt and the soaring inequality, the 1980s has seen a com-pletely new identity of the consumer behaviour, previously mitigated by the 1960s protests of the Civil Rights Movement and the ecological movements. This new identity of consumption behaviour has led to the the energy-consuming society, that, after the fall of the Eastern Bloc, has spread all over the world.

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34 CHAPTER 4. USA EMPIRICAL ANALYSIS Analysing the US can be an essential starting point to understand if energy has a pivotal role in economic growth.

4.1 Variables

Before analyzing the empirical results, it is better to focus on the variables taken into account and their sources.

The database take into account 55 years, from 1960 to 2014, the analysis is based on annual time series.

Variables taken into account are GDP, GDP per capita, capital stock, av-erage annual hours worked, employment, total avav-erage annual hours worked and primary energy consumption.

Except primary energy consumption, which its source is the US Energy Information Administration (EIA) database, all variables are taken by Penn World Table of the University of Groningen.

US real GDP 1960−2014 time series

Time Billions of 2011 US$ 1960 1970 1980 1990 2000 2010 40000 80000 120000 160000

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4.1. VARIABLES 35 GDP, GDP per capita and capital stock are expressed in real terms at constant 2011 US dollars.

GDP per capita is calculated by dividing GDP over population, a data from Penn World Table.

Employment refers to how many workers are engaged, average annual hours worked expresses the average amount of hours worked by a single worker, while total average annual hours worked measure the amount of hours worked by all the employed in the economy.

Primary energy is expressed in BTU and it measures the total energy de-mand of a country, and it covers consumption of the energy sector, losses during transformation and distribution of energy, and the final consumption by end users.

US GDP grew from 32901 billions of 2011US$ in 1960 to 164902 billions of 2011US$ in 2014.

It is possible to address five different year breakpoints: 1967, 1977, 1987, 1996 and 2004, while the confidence interval are just one or two years before and after the breakpoints.

From figure 4.1, it is clear that GDP level has been easily recovered after the oil crisis, 1982 recession and the Dot-com bubble, while it takes more years to recover from the 2007-2008 financial crisis.

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36 CHAPTER 4. USA EMPIRICAL ANALYSIS

US GDP per capita 1960−2014 time series

Time 2011 US$ 1960 1970 1980 1990 2000 2010 20000 30000 40000 50000

Figure 4.2: US GDP per capita time series

US GDP per capita grew from 17384 2011US$ in 1960 to 51620 2011US$ in 2014.

The figure shows the same breakpoints of GDP for GDP per capita time series.

Unfortunately, GDP, and so GDP per capita, it is not a wellness indicator and it does not take into account inequality.

GDP per capita value is related to the evolution of the population; US pop-ulation rose from 185 million in 1960 to 320 million in 2014, but even this increase GDP has grown more in order to sustain the constant GDP per capita growth.

The GDP per capita downturns are in relation with the previously cited eco-nomic recessions, but, conversely to the GDP series, GDP per capita has decreased during the first Gulf War in 1990-1991.

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4.1. VARIABLES 37 US capital stock 1960−2014 Time Billions of 2011US$ 1960 1970 1980 1990 2000 2010 10000 20000 30000 40000 50000

Figure 4.3: US capital stock time series

US capital stock grew from 10803 billions of 2011US$ in 1960 to 51190 billions of 2011US$ in 2014. The growth of capital stock has been linear and in 55 years it has quintupled its value.

Conversely to the GDP and GDP per capita time series, capital stock has not been affected by the 19th century crisis, but it is clear from figure 4.3 that after the 2007-2008 financial crisis the time series bend towards a lower slope.

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US primary energy consumption 1960−2014 time series

Time Quadr illion of BTU 1960 1970 1980 1990 2000 2010 50 60 70 80 90 100

Figure 4.4: US primary energy consumption time series

Primary energy consumption grew from 45 quadrillions of BTU in 1960 to 98 quadrillions of BTU in 2014. In 55 years primary energy consumption doubled, but its path has been less and less linear and it follows many cycles. BTU is the British Termal Unit, the Anglo-Saxon unit of heat and, since heat is known to be an equivalent of energy, it can be used to measure primary energy.

Before 1973, energy consumption grew linearly until it reached the first peak for the first oil crisis. Energy consumption has been reduced until 1975 and then it started to grow and to reach a new peak in 1980.

After the second oil crisis, during the 1982 economic recession, energy con-sumption has reached the level of 1975 energy concon-sumption, and it slowly recovered its pre-1979 crisis only in the late 1980s.

From the late 1980s to 2001, energy consumption grew constantly, facing a plateau during the First Gulf War years.

From 2001, energy consumption has not been clear, but facing a big downturn after the 2007-2008 financial crisis.

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4.1. VARIABLES 39

US average annual hours worked by worker 1960−2014 time series

Time Hours 1960 1970 1980 1990 2000 2010 1800 1850 1900 1950

Figure 4.5: US average annual hours worked by worker time series Average annual hours worked has seen a reduction from 1948 average hours worked in 1960 to 1786 average hours worked in 2014.

Until 1966, hours worked followed an increasing trend, that has been followed by a decreasing path until 1982. From 1983 to 1999, it followed a cyclical pattern of upturn and downturn.

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Numbers of people employed in the US 1960−2014 time series

Time series Millions of w or k ers 1960 1970 1980 1990 2000 2010 80 100 120 140

Figure 4.6: US numbers of employed time series

People employed grew from 71 millions of workers to 148 millions. The greatest downturn happened after the 2007-2008 financial crisis, while for the rest of the time series the downturns related to other crisis have been recovered in a short period.

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4.2. ENERGY RATIOS 41

Total average annual hours worked US 1960−2014 time series

Time series Millions of hours 1960 1970 1980 1990 2000 2010 140000 180000 220000 260000

Figure 4.7: US total average hours worked time series

Total average annual hours worked is simply given by multiplying the time series of average annual hours worked by a single worker for the time series of numbers of people employed, and it can be seen as an interaction variable.

The time series is growing over time since it is driven by the increase of num-bers of employed.

Since the average annual hours worked has displayed a constant reduction over time, a simple downturn in the number of employed during the eco-nomic recessions, total average annual hours has faced bigger downturn with respect to the number of employed variable.

4.2 Energy ratios

In order to better understand how energy evolved through the time series, I decided to plot the the ratio between energy and the other variables and to show the structural break in the different time series.

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trans-42 CHAPTER 4. USA EMPIRICAL ANALYSIS formed in dimensionless time series, using the 1960 as pivotal year.

In this work I am not computing the BTU per dollar (or per capital or per hours or per worker), but using the plot to understand the behaviour of the ratio.

US energy/gdp 1960−2014 time series

Time energy/gdp 1960 1970 1980 1990 2000 2010 0.5 0.6 0.7 0.8 0.9 1.0

Figure 4.8: US energy/gdp ratio time series

Figure 4.7 shows the energy efficiency. From the time series is clear that the economy has become more and more productive, by using an increasing amount of energy. Even if US economy energy consumption has increased (see figure 4.4), the ratio has decreased due to the huge expansion of US GDP.

Energy efficiency has been decreased during the overall time series, as being reduced by more than the half. From this evidence it seems that energy efficiency has been reduced, but the reason is uncertain due to the aggregation nature of the variable.

The increase of GDP can be caused by other factors and not energy by itself, but the pattern does not display a better use of energy, due to the unclear distribution of the use of energy.

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US energy/gdp per capita 1960−2014 time series

Time

energy/gdp per capita

1960 1970 1980 1990 2000 2010

0.8

0.9

1.0

1.1

Figure 4.9: US energy/gdp per capita ratio time series

Figure 4.8 shows the per capita energy efficiency. Until 1973-1974 energy consumption grew more than GDP per capita.

From 1980 we have the opposite pattern and GDP per capita started to grow more than energy, meaning that GDP per capita has become more productive in terms of energy consumption.

From 1987 to 1996, energy consumption and GDP per capita grew more or less the same, but then GDP per capita grew more rapidly than energy consumption.

The energy efficiency per capita has seen a minor reduction with respect to the aggregate one, and probably driven by the increase in population.

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US energy/capital stock 1960−2014 time series

Time energy/capital stock 1960 1970 1980 1990 2000 2010 0.5 0.6 0.7 0.8 0.9 1.0

Figure 4.10: US energy/capital ratio time series

Figure 4.9 shows the energy efficiency related to capital stock. The plot displays a similar pattern to the one showed for the energy efficiency of figure 4.7, so capital stock has become more and more energy efficient.

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US energy/average hours worked 1960−2014 time series

Time energy/a v er age hours w or k ed 1960 1970 1980 1990 2000 2010 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Figure 4.11: US energy/average hours ratio time series

Figure 4.10 shows the ratio between energy consumption and annual av-erage hours worked.

As seen before, energy consumption grew constantly , while average hours worked has been reduced through the time series.

As a result it is possible to state that energy worked as a substitute for hours worked, enhancing the role of automation and labor saving technology fuelled by energy consumption that drove the average hours worked to its minimum.

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US energy/employment 1960−2014 time series

Time energy/emplo yment 1960 1970 1980 1990 2000 2010 1.00 1.05 1.10 1.15 1.20 1.25 1.30

Figure 4.12: US energy/numbers of employed ratio time series

Figure 4.11 shows the ratio between energy and number of employed. Un-til 1973-1974 energy grew faster than number of employed, then it is possible to see a catch up in the growth of number of employed in relation of the huge decrease in the ratio until 1985.

From 1985, the situation remained quite stable, with some fluctuations, but energy growth was greater than growth of number of employed through all the time series.

It is possible to see two different regimes, before and after 1970s oil crisis, since after the oil crisis it was possible to create ”jobs” by consuming less energy than the previous regime.

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US energy/total average hours worked 1960−2014 time series

Time energy/total a v er age hours 1960 1970 1980 1990 2000 2010 1.0 1.1 1.2 1.3

Figure 4.13: US energy/total average annual hours ratio time series The ratio between energy and total average annual hours worked displays a similar pattern to the one showed for the ratio related to employment. With respect to the previous figure, the ratio is higher, meaning that total average hours worked has grown less than number of the employment. In order to sustain the pattern of increasing number of workers and the reduction of average annual hours worked, energy had to grow more than the interaction variable.

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Chapter 5 LINEX estimation

Starting from the LINEX function in 3.24, to use normalized variables yt= Yt Y0 ; kt = Kt K0 ; lt= Lt L0 ; et= Et E0 (5.1) where the variable with the subscript 0 refers to the first year of the time period we analyze, then the LINEX function becomes

yt= et× exp n at× h 2 −lt+ et kt i + atct× l_t et − 1o . (5.2) In estimating the technology parameter y is GDP per capita, c is capital stock, l is total average annual hours worked and e is primary energy con-sumption.

In order to express the LINEX function in more clear terms, we express the LINEX by using logarithm:

lnyt et = at× h 2 −lt+ et kt i + atct× l_t et − 1 ; (5.3)

where lnyt_et is the logarithm of the inverse of energy efficiency, and by expressing lnyt et = yt; 2 − lt+ et kt = xt; atct = bt and lt et − 1 = zt (5.4) the LINEX finally becomes the starting point for the econometric model

yt= atxt+ btzt . (5.5)

In the econometric models at will be represented by β1 and bt by β2.

The technological parameter ctwill be computed by dividing the estimate β2 49

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50 CHAPTER 5. LINEX ESTIMATION for β1.

Reminding that atis the technological parameter related to capital effective-ness of activation of capital and its handle with labor by using energy, while ct is the energy demand of fully employed capital stock.

5.1 Oil price

In his papers, Kummel fitted the technology parameters by minimizing the sum of squared errors, so reducing the deviations between the theoretical curves from the empirical growth curves.

He modeled a and c by using logistic function and Taylor series expansion. In table 5.1 are reported its estimates for the technological parameters.

Table 5.1: US Kummel’s results 1960-1996

a1 a2 a3 a4 c1 c2 c3 c4

Parameters 0.21 0.49 0.97 22.64 2.63 0.81 0.81 22.24

My goal is trying to estimate the two technology parameters by using econometric models, subdividing the time framework in relation to the trend of real oil prices, since an increase in real oil prices could be followed by a different regime on energy conversion technology.

In figure 4.12, I plotted the logarithm of real oil price. The figure shows also the structural break of the time series.

Since the breakpoints are in 1974, 1985 and 2004, I decided to subdivide my analysis for the following different time period:

• 1960-2014; • 1960-1974; • 1975-1985; • 1986-2004; • 2005-2014.

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5.2. STATIC MODEL REGRESSION 51

US logarithm real oil prices time−series

Year ln real oil pr ices 1970 1980 1990 2000 2010 3.0 3.5 4.0 4.5

Figure 5.1: Logarithm real oil prices

5.2 Static model regression

Expressing the LINEX as a static model, and it describes a contemporaneous relation between the dependent variable yt and the regressors xt and zt. The static model can be written as:

yt= β0+ β1xt+ β2zt+ ut (5.6) In order to be clear, R2 results will be taken into account and commented on the paragraph related to the Durbin-Watson statistics.

In table 5.2 are shown all the results from the static model regression for the overall period and for the time periods derived from the subdivision related to the oil price structural break.

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52 CHAPTER 5. LINEX ESTIMATION For the time period 1960-2014, we obtain two highly significant results for the estimation of the technological parameter.

Since at is equal to 0.364 and bt is 0.837, the energy parameter ct is 2.30.

Moving the analysis to the shorter time interval (due to the oil price breakpoints), we reduce the number of observations from 55 to an interval between 10 and 19.

This reduction of numbers of observation may affect the significance of the results.

For the period 1960-1974 the coefficient related to at is 0.168 it is slightly statistically significant, while bt is highly statistically significant level with a coefficient equal to 0.638.

The estimated coefficients for ct is 3.797

The results are similar to the one related to the overall period.

For the period related to 1975-1985, the coefficient for atis not significant and it displays a negative value of -0.177, while for bt the result is highly significant and it is 1.319.

The negative value of at moves against the theoretical assumptions made by Kummel, since it is impossible to address a negative capital efficiency related to energy activation.

Due to the negative value of at, it is impossible to evaluate ct.

For the time period 1986-2004 atdisplays a value of 0,359 and bt is 1,047, so ct is 2,92.

For 2005-2014, at displays a coefficient of 0,104, with a highly statisti-cally significance level. On the other hand bt is 0,7. Both results are highly significant

Computing ct, its value is 6,731.

The period 2005-2014 can be seen as a period in which capital stock ef-fectiveness is at its minimum, while the energy demand of capital stock is at its maximum, and it can be seen as a reflection of the ICT revolution merged with the economic downturn related to the 2007-2008 financial crisis.

LINear EXponential function: energy as factor of production A USA empirical analysis